Analysis of Signal Reconstruction Algorithms Based on Consistency Constraints
Lee, Chang Hsin
:
2017-06-19
Abstract
A fundamental problem in signal processing called signal reconstruction, or signal recovery, is the determination of a signal from a sequence of samples obtained
from the signal. The sampling process can be viewed as obtaining measurements from
a set of measurement vectors in an N-dimensional space. Studies on the reconstruction problem have resulted
in major breakthroughs in technology in the past century, and practical solutions to the
problem are still essential in the advancement of fields such as image processing and speech
recognition.
Consistent reconstruction and Rangan-Goyal algorithm are two algorithms that produce
estimates of a signal from consistency constraints when the measurements are
corrupted with i.i.d uniformly distributed noises. Under the assumption that the
measurements are taken with i.i.d. unit-norm random vectors, the second error moments
of both algorithms are known to converge with a rate of O(N^2). In this work, we showed
that the general p-th error moments of both algorithms converge with a rate of O(N^p)
under general admissibility conditions on the sampling distribution that no longer require
the measurement vectors to be unit-norm.